CN110674577A - New energy automobile high-rotating-speed bearing dynamic parameter acquisition method - Google Patents

Abstract

The invention relates to a new energy automobile high-rotating-speed bearing dynamic parameter acquisition method, which comprises the following steps: s1, setting bearing parameters and bearing working conditions; s2, only considering the axial load of the bearing, and iteratively solving the contact angle convergence value only under the axial force through a load-contact angle change formula: s3, considering the radial load and the axial load simultaneously; s4 solving radial displacement delta_rAnd axial displacement delta_a(ii) a S5, carrying out statics analysis on the bearing, and establishing a static balance equation of the bearing; and S6, considering the centrifugal force, gyro moment and Hertz contact of the bearing, establishing a bearing statics model and obtaining bearing dynamic parameters. The invention can rapidly obtain bearing dynamic parameters, greatly improves the working efficiency, and plays an important role in the optimization design of the high-speed bearing and the analysis design of the dynamic characteristics of the high-speed rotor-bearing system.

Description

New energy automobile high-rotating-speed bearing dynamic parameter acquisition method

Technical Field

The invention relates to the field of bearing dynamics, in particular to a new energy automobile high-rotating-speed bearing dynamics parameter acquisition method.

Background

With the development of new energy automobile technology, the development of high-rotating-speed motor bearing analysis technology is urgently needed. Therefore, a method for accurately evaluating the mechanical property of the high-rotating-speed bearing of the new energy automobile with the initial value is needed.

At present, a bearing statics analysis method provided by Jones based on a raceway control theory is widely used for bearing mechanical property analysis. The initial value selected in the method has a large influence on the model convergence effect, and an analyst needs to have sufficient initial value setting experience.

According to the literature, a statics calculation optimization result is used as a statics iteration initial value, a combined iteration algorithm combining a Newton-Raphson method and a Broyden method is provided, selection is still needed according to experience or existing experimental data, the experiment cost is high, and the experience accuracy is low.

Although the Chinese patent 'a method for solving numerical value of high-speed angular contact ball bearing (application number 201711429560.9)' adopts setting intermediate variable, iterative correction factor, simplifying Jacobian matrix and the like to solve the bearing statics equation, the radial and axial displacement delta still needs to be set_rAnd delta_aAnd the initial value of the angular displacement theta does not indicate whether the calculation result of the method is consistent and accurate with the calculation result of the reliable Newton-Raphson method.

Disclosure of Invention

The invention aims to solve the technical problem of providing a dynamic parameter acquisition method for a high-speed bearing of a new energy automobile, accurately calculating an initial value of a ball bearing quasi-static equation through a steel ball load-contact angle calculation formula and a ball bearing static equation, and further efficiently, quickly and reliably solving the mechanical property parameter of the high-speed bearing through a Levenberg-Marquardt method.

The technical scheme adopted by the invention for solving the technical problems is as follows: a dynamic parameter acquisition method for a new energy automobile high-speed bearing is constructed, and comprises the following steps:

s1, setting bearing parameters and bearing working condition F ═ F_aF_rM]In which F is_aFor axial loading, F_rRadial load, M is the applied moment;

s2, only considering the axial load of the bearing, and iteratively solving a contact angle convergence value alpha' when only the axial force is applied through a load-contact angle change formula (1), wherein the formula (1) is as follows:

wherein alpha is the initial contact angle, Z is the number of rollers, D is the diameter of the steel ball, f_mThe curvature of the average groove of the raceway and the deformation coefficient of the contact zone are c;

s3, taking into account both the radial load and the axial load, and substituting α' calculated in step S2 as an initial iterative value of α ″ into the load-contact angle variation formula (2) to iteratively solve the initial contact angle α ″, where the formula (2) is:

wherein ε is a load distribution parameter, J_aIntegrating the load distribution;

s4, formula F_a＝ZQ_maxJ_asin alpha' calculation of maximum load Q_maxThe maximum displacement delta is obtained from the elastic deformation relationship_maxIs substituted into the formula delta_max＝δ_asinα″+δ_rcos α "andsimultaneous solution to radial displacement delta_rAnd axial displacement delta_a；

S5, carrying out statics analysis on the bearing, establishing a static balance equation of the bearing, and solving the radial displacement delta obtained in the step S4_rAnd axial displacement delta_aThe method is used as an iterative calculation initial value of the static equilibrium equation of the bearing until convergence, the static parameters are solved, and a group of approximate solutions of the static calculation is estimated according to the elastic deformation relation and the geometric relation

S6, establishing a shaft by considering centrifugal force, gyroscopic moment and Hertz contact of the bearingBearing a static model to approximate a solution

And substituting the initial value into the solution until convergence, thus obtaining the dynamic parameters of the bearing.

In the foregoing solution, in step S2, the method further includes: calculating the convergence accuracy of α', if

The next step is executed ifThe calculation is repeated until convergence; where i is the number of iterations and e is the convergence accuracy.

In the foregoing solution, in step S3, the method further includes: calculate the convergence accuracy of α ″, if

The next step is executed if

The calculation is repeated until convergence; where i is the number of iterations and e is the convergence accuracy.

The method for acquiring the dynamic parameters of the new energy automobile high-speed bearing has the following beneficial effects:

according to the method, approximate solutions of a group of quasi-static equations are accurately estimated through theoretical mechanics analysis to serve as initial values of iterative computation, the solving efficiency is greatly improved, the condition that the solving process is slow in convergence or even not is avoided, the dynamic parameters of the angular contact ball bearing can be quickly obtained only by inputting the working conditions and parameters of the bearing, the working efficiency is greatly improved, and the method plays an important role in optimization design of a high-speed bearing and analysis design of the dynamic characteristics of a high-speed rotor-bearing system.

Drawings

The invention will be further described with reference to the accompanying drawings and examples, in which:

FIG. 1 is a flow chart of a dynamic parameter obtaining method for a high-speed bearing of a new energy automobile according to the invention;

FIG. 2 is a graph of inner race displacement versus contact angle for a purely radial load;

FIG. 3 is a graph of inner race displacement versus contact angle under a combined load;

FIG. 4 is a graph showing the change in the center of curvature of the anterior and posterior grooves under load;

FIG. 5 is a steel ball diagram;

FIG. 6 is a graph of contact angle as a function of axial force;

FIG. 7 is a graph of axial displacement versus axial force.

Detailed Description

For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

As shown in fig. 1, for the angular contact ball bearing with given working conditions and basic structural parameters, the new energy automobile high-speed bearing dynamics parameter obtaining method of the invention can be mainly divided into the following 3 steps according to the iterative calculation times of the flow of fig. 1:

the method comprises the following steps: firstly, the radial and axial displacement delta of the inner ring of the bearing is obtained by adopting a theoretical mechanics method_aAnd delta_rThe bearing outer ring is fixed and the load is F ═ F_aF_rM],(F_aFor axial loading, F_rRadial load, M applied moment);

when the inner ring is only subjected to axial force, the displacement of the inner ring is schematically shown in figure 2. The curvature center of the outer raceway groove is E, the curvature center of the inner raceway groove moves from I to I 'under the action of load, the contact angle is changed from alpha to alpha',

is displaced by δ axially_a，

Is a normal approach delta_n(where the amount of deformation is equal at all angular positions), f_i、f_eRespectively an inner raceway and an outer racewayThe ratio D is the diameter of the steel ball;

the geometrical relation and the contact deformation relation are as follows:

wherein ε is a load distribution-related parameter, the mean groove curvature f_m＝0.5(f_i+f_e) C is the contact zone deformation coefficient (c is 4.948), Z is the number of rollers, J_aTo relate to F_rtanα/F_aThe integral value of (a);

by calculating F_rtanα/F_aLooking up the table to obtain ε and J_a. At this time, due to the pure axial load, ε → + ∞, J _a1, formula (1):

for the formula (2), the initial contact angle alpha DEG is used as an iterative initial value, iterative solution is carried out until convergence is achieved, and since the radial displacement is small relative to the axial displacement, the alpha' value is close to the value of the contact angle changed under the simultaneous action of the radial load and the axial load, the value is used as the initial value of the next iterative calculation, and the calculation efficiency can be improved.

On the basis of the above analysis, the consideration of the radial force F is increased_rIn the schematic diagram (the position angle psi is equal to 0 deg.) as shown in fig. 3, the curvature center E of the outer raceway groove is fixed, the curvature center of the inner raceway groove is moved from I to I' by the axial force and then moved to I "by the radial force, the contact angle is changed from alpha to alpha",

is displaced by δ axially_a，

Is a radial displacement delta_r，

Is a maximum displacement delta_max；

When α - α "is small, the relationship between the geometric relationship and the contact deformation is:

by calculating F_rtanα/F_aLooking up the table to obtain ε and J_aAnd taking alpha ' as an initial value, iteratively calculating a computational formula to obtain a final contact angle alpha ' under the action of the radial load and the axial load, and substituting the obtained contact angle alpha ' into the following equation to obtain radial displacement and axial displacement:

F_a＝ZQ_maxJ_asinα″ (5)

δ_max＝δ_asinα″+δ_rcosα″ (6)

calculated delta_aAnd delta_rUnder static load F only_aAnd F_rAmount of displacement of down, but delta_aAnd delta_rRelatively close to combined load [ F ]_aF_rM]Under the action, the radial and axial displacement values of the inner ring of the bearing are used as initial values of statics iterative calculation, so that the low calculation efficiency caused by depending on experience value can be avoided.

Step two: under the condition that centrifugal force and gyro moment are not considered, the bearing inner ring is subjected to static force analysis, and a static force balance equation of the bearing inner ring is established:

wherein psi_jIs the position angle, alpha is the contact angle, Z is the number of rollers, d_mFor bearing pitch diameter

The distance S between the curvature centers of the inner and outer grooves after the bearing is loaded can be obtained through the contact geometric relationship between the ball and the raceway:

S＝((Asinα°+δ_a+R_icosψ_j)²+(Acosα°+δ_rcosψ_j)²)^1/2(11)

wherein A is the distance between the curvature centers of the initial inner and outer grooves, alpha is the initial contact angle, and the related parameters are calculated as follows:

A＝(f_i+f_e-1)D (12)

R_i＝0.5D+(f_i-0.5)Dcosα° (13)

from the load-deformation relationship Q ═ K_nδⁿ(K_nNormal contact stiffness), the position angle psi_jContact force of (c):

at an arbitrary position angle psi_jThe trigonometric relationship may be determined by the following relationship:

obtaining the displacement [ delta ] by solving the static equilibrium equation sets (8) - (10)_aδ_rθ]^TBased on this substitution into the following equation, a set of approximate solutions for the statics calculation is found:

X_ij＝((f_i-0.5)D+δ_ij)sinα (19)

X_oj＝((f_o-0.5)D+δ_oj)cosα (20)

wherein, K_piAnd K_poJ is 1, 2, 3.. Z (Z is the number of steel balls) which is the contact rigidity of the inner and outer raceways.

Compared with the statics analysis, the statics analysis does not consider dynamic factors such as centrifugal force, gyro moment and the like, but a group of statics calculation initial values estimated through statics calculation parameters are closer to a real solution of the statics calculation, so that certain rationality is achieved, and the condition that convergence is slow or even does not converge caused by unreasonable experience values can be prevented. Will take the above valuesThe initial value of the statics calculation is substituted into the statics model for iterative solution, and the reliability of the statics iterative solution can be well guaranteed.

Step three: and establishing a bearing statics model, and solving kinetic parameters through iterative calculation.

Firstly, the schematic diagram of the change of the curvature centers of the inner and outer raceway grooves after the bearing is loaded is shown in fig. 4, and the following geometrical relationships are provided:

A_1j＝Asinα°+δ_a+R_iθcosψ_j(21)

A_2j＝Acosα°+δ_rcosψ_j(22)

using the pythagorean theorem, the following geometric coordination equation exists:

(A_1j-X_1j)²+(A_2j-X_2j)²-[(f_i-0.5)D+δ_ij]²＝0 (23)

angular position psi_jIn the steel ball force diagram shown in fig. 5, the contact load and the contact deformation of the steel ball at the contact point are in the following relationship:

establishing a steel ball balance equation set:

according to the track control theory, the outer raceway control is carried out at high speed, and lambda is taken_ij＝0，λ_ojWhere the trigonometric function may be calculated by the following formula:

in the steel ball equation system, beta can be obtained based on pure rolling hypothesis,

And

the centrifugal force and gyro moment are calculated as follows:

and finally, establishing a force balance equation set of the whole bearing:

the geometric coordination equation set, the steel ball balance equation set and the bearing balance equation set are simultaneously solved based on Matlab until convergence, so that bearing dynamic parameters can be obtained, fatigue life, bearing rigidity and load distribution can be calculated based on the bearing dynamic parameters, and technical support can be provided for the analysis and design of the dynamic characteristics of the high-speed bearing-rotor system.

According to the above calculation procedure, example calculations were performed for the 7218 angular contact ball bearing shown in table 1.

TABLE 1

When the bearing rotation speed is 15000rpm, the calculation results are shown in fig. 6 and 7, the accuracy of the calculation results is verified by comparing with the Harris calculation results, because the selected bearing parameters may have errors in the Harris model parameters, and may not be completely the same as the calculation results, but the overall calculation accuracy is satisfactory, the two groups of calculation results respectively have the same coefficient as the Harris results shown in table 2 (the closer the coefficient is to 1, the better the conformity is shown), and the coefficient calculation formula is as follows:

(X, Y are two sets of comparison data, and n is the number of data).

TABLE 2

In order to verify the calculation efficiency, a high-speed angular contact ball bearing B7008C/P4 is selected, and the bearing parameters are shown in Table 3.

TABLE 3

The pre-tightening force is set to be 290N, the radial loads are respectively 0, 50 and 100N, 20 rotating speed working conditions of 1000, 2000 and … … 20000r/min are calculated through Matlab programming, because the Jones-Harris model is most representative (JHM model for short), and the model is generally solved through a Newton-Raphson method, the average calculation time of the statics is compared with the JHM method, the result shows that after the method is adopted, because the initial value is closer to the real solution, the iterative calculation efficiency is greatly accelerated, and the JHM method is compared with the method disclosed by the invention as shown in the table 4.

TABLE 4

While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (3)

1. A new energy automobile high-speed bearing dynamic parameter obtaining method is characterized by comprising the following steps:

s1, setting bearing parameters and bearing working condition F ═ F_aF_rM]In which F is_aFor axial loading, F_rRadial load, M is the applied moment;

s2, only considering the axial load of the bearing, and iteratively solving a contact angle convergence value alpha' when only the axial force is applied through a load-contact angle change formula (1), wherein the formula (1) is as follows:

wherein alpha is the initial contact angle, Z is the number of rollers, D is the diameter of the steel ball, f_mThe curvature of the average groove of the raceway and the deformation coefficient of the contact zone are c;

s3, taking into account both the radial load and the axial load, and substituting α' calculated in step S2 as an initial iterative value of α ″ into the load-contact angle variation formula (2) to iteratively solve the initial contact angle α ″, where the formula (2) is:

wherein ε is a load distribution parameter, J_aIntegrating the load distribution;

s4, formula F_a＝Z_QmaxJ_asin alpha' calculation of maximum load Q_maxThe maximum displacement delta is obtained from the elastic deformation relationship_maxIs substituted into the formula delta_max＝δ_asinα″+δ_rcos α "andsimultaneous solution to radial displacement delta_rAnd axial displacement delta_a；

S5, carrying out statics analysis on the bearing, establishing a static balance equation of the bearing, and solving the radial displacement delta obtained in the step S4_rAnd axial displacement delta_aThe method is used as an iterative calculation initial value of the static equilibrium equation of the bearing until convergence, the static parameters are solved, and a group of approximate solutions of the static calculation is estimated according to the elastic deformation relation and the geometric relation

S6, considering the centrifugal force, gyro moment and Hertz contact of the bearing, establishing a bearing statics model to approximate a solution

And substituting the initial value into the solution until convergence, thus obtaining the dynamic parameters of the bearing.

2. The method for acquiring dynamic parameters of the high-speed bearing of the new energy automobile according to claim 1, wherein the step S2 further includes: calculating the convergence accuracy of α', if

The next step is executed if

The calculation is repeated until convergence; where i is the number of iterations and e is the convergence accuracy.

3. The method for acquiring dynamic parameters of the high-speed bearing of the new energy automobile according to claim 1, wherein the step S3 further includes: calculate the convergence accuracy of α ″, if

The next step is executed ifThe calculation is repeated until convergence; where i is the number of iterations and e is the convergence accuracy.

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